Check all of the following that are true for the series
∑n=1∞(n−3)cos(n*π)n^2
A. This series converges B. This series diverges C. The integral
test can be used to determine convergence of this series. D. The
comparison test can be used to determine convergence of this
series. E. The limit comparison test can be used to determine
convergence of this series. F. The ratio test can be used to
determine convergence of this series. G. The alternating series
test can be...
1. Given the series:
∞∑k=1 2/k(k+2)
does this series converge or diverge?
converges
diverges
If the series converges, find the sum of the series:
∞∑k=1 2/k(k+2)=
2. Given the series:
1+1/4+1/16+1/64+⋯
does this series converge or diverge?
diverges
converges
If the series converges, find the sum of the series:
1+1/4+1/16+1/64+⋯=
1. a.) Find the values of x for which the series converges.
Express your answer in interval notation. n = 1 ∞
∑(−3)n?n
b.) Find the sum of the series (valid over the values of x found
in part a).
Determine if the following series converge or diverge. If it
converges, find the sum.
a. ∑n=(3^n+1)/(2n) (upper limit of sigma∞, lower limit is
n=0)
b.∑n=(cosnπ)/(2) (upper limit of sigma∞ , lower limit is n=
1
c.∑n=(40n)/(2n−1)^2(2n+1)^2 (upper limit of sigma ∞ lower limit
is n= 1
d.)∑n = 2/(10)^n (upper limit of sigma ∞ , lower limit of sigma
n= 10)
Find the values of p for which the series is convergent
(a) Σ(n=2 to ∞) 1/n(ln n)^p
(b) Σ(n=2 to ∞) n(1+n^2)^p
HINT: Use the integral test to investigate both
Consider the series X∞ k=3 √ k/ (k − 1)^3/2 . (a) Determine
whether or not the series converges or diverges. Show all your
work! (b) Essay part. Which tests can be applied to determine the
convergence or divergence of the above series. For each test
explain in your own words why and how it can be applied, or why it
cannot be applied. (i) (2 points) Divergence Test (ii) Limit
Comparison test to X∞ k=2 1/k . (iii) Direct...
for (i=0; i<n; i++)
for (j=1; j<n; j=j*2)
for (k=0; k<j; k++)
... // Constant time operations
end for
end for
end for
Analyze the following code and provide a "Big-O" estimate of
its running time in terms of n. Explain your analysis.
Note: Credit will not be given only for answers - show all
your work:
(2 points) steps you took to get your answer.
(1 point) your answer.
What are the significance of bandstructure (E-k) plots?
Which information we can get from E-k plots (obtained from DFT
analyses) for materials? Please explain in details with some
relevant diagrams or plots.